We search for a light Higgs boson A⁰ in the fully reconstructed decay chain of J/ψ → γA⁰, A⁰ → μ⁺μ⁻ using (225.0 ± 2.8) ×106 J/ψ events collected by the BESIII experiment. The A⁰ is a hypothetical CP-odd light Higgs boson predicted by many extensions of the Standard Model including two spin-0 doublets plus an extra singlet. We find no evidence for A⁰ production and set 90% confidence-level upper limits on the product branching fraction ℬ(J/ψ → γA⁰) × ℬ(A⁰ → μ⁺μ⁻) in the range of (2.8-495.3) ×10⁻⁸ for 0.212 ≤ mA⁰ ≤ 3.0 GeV/c². The new limits are five times below our previous results, and the nature of the A⁰ is constrained to be mostly singlet.